Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9751	(17*10^88761-41)/3	88762	Robert Price	09/2017
9752	(2^294834+2854)/2	88754	Stefano Morozzi	01/2020
9753	(2^294823+2466)/2	88751	Stefano Morozzi	01/2020
9754	(2^294764+642)/2	88733	Stefano Morozzi	01/2020
9755	2^294754+15015	88730	Lelio R Paula	10/2013
9756	(3^185951-7)/20	88720	Lelio R Paula	01/2013
9757	(2^294688+3186)/2	88710	Stefano Morozzi	01/2020
9758	(2^294673+3906)/2	88706	Stefano Morozzi	01/2020
9759	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
9760	(2^294631+2514)/2	88693	Stefano Morozzi	01/2020
9761	(10^88680+11)/3	88680	Robert Price	11/2014
9762	2*7^104928-9	88675	Lelio R Paula	10/2014
9763	11^85150+12	88675	Lelio R Paula	11/2015
9764	8*6^113951+5	88673	Lelio R Paula	10/2014
9765	(2^294549+3110)/2	88668	Stefano Morozzi	01/2020
9766	6*10^88665-79	88666	Robert Price	03/2022
9767	6^113940-18563	88663	Enzo Doria	03/2013
9768	38^56123-56123^38	88663	Norbert Schneider	02/2017
9769	2^294492-65	88651	Lelio R Paula	10/2012
9770	(2^294481+2822)/2	88648	Stefano Morozzi	01/2020
9771	23874^5165+5165^23874	88646	Hans Havermann	08/2020
9772	(2^294469+1466)/2	88644	Stefano Morozzi	01/2020
9773	7*10^88634-27	88635	Dylan Delgado	08/2019
9774	20^68120-53	88627	Lelio R Paula	01/2016
9775	122^42477-121	88623	Norbert Schneider	10/2018
9776	2^294391-113257	88621	Enzo Doria	07/2014
9777	5^126784-15476	88619	Enzo Doria	02/2013
9778	(2^294335+554)/2	88604	Stefano Morozzi	01/2020
9779	2^294327+9	88602	Lelio R Paula	10/2012
9780	2^294320+18915	88600	Lelio R Paula	10/2013
9781	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
9782	(5*10^88595+103)/9	88595	Robert Price	04/2022
9783	20723^18834+18834^20723	88590	Hans Havermann	08/2020
9784	(68*10^88586-329)/9	88587	Robert Price	03/2021
9785	(2^294268+1402)/2	88584	Stefano Morozzi	01/2020
9786	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
9787	6*10^88571+77	88572	Robert Price	06/2020
9788	2^294224-933075	88571	Paul Bourdelais	04/2021
9789	(2^294145+1346)/2	88547	Stefano Morozzi	01/2020
9790	(2*10^88545+7)/9	88545	Erik Branger	03/2011
9791	2^294137-133	88545	Lelio R Paula	10/2012
9792	(2^294109+3494)/2	88536	Stefano Morozzi	01/2020
9793	23515^5818+5818^23515	88529	Hans Havermann	08/2020
9794	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
9795	4^147036+147036^4+1	88525	Robert Price	04/2014
9796	22541^8458+8458^22541	88525	Hans Havermann	08/2020
9797	(14^77213-5^77213)/9	88496	Robert Price	04/2013
9798	2^293965+2793377	88493	Enzo Doria	03/2016
9799	(2^293956+3306)/2	88490	Stefano Morozzi	01/2020
9800	11^84971-150	88489	Enzo Doria	08/2012
9801	(2^293944+1066)/2	88486	Stefano Morozzi	01/2020
9802	9*10^88485+91	88486	Robert Price	10/2020
9803	48^52626-47	88478	Norbert Schneider	08/2018
9804	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
9805	11^84958-2190	88475	Enzo Doria	12/2012
9806	(2^293902+3070)/2	88474	Stefano Morozzi	01/2020
9807	(35*10^88471-89)/9	88472	Robert Price	02/2022
9808	2^293880-111347	88467	Enzo Doria	05/2014
9809	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
9810	10^88457+278733	88458	Patrick De Geest	07/2017
9811	10^88457-401	88457	Robert Price	06/2017
9812	(2^293834+3018)/2	88453	Stefano Morozzi	01/2020
9813	(2^293747+1626)/2	88427	Stefano Morozzi	01/2020
9814	22080^10109+10109^22080	88424	Hans Havermann	08/2020
9815	11^84908-1680	88423	Enzo Doria	12/2012
9816	(2^293703+3486)/2	88414	Stefano Morozzi	01/2020
9817	2^293679-112075	88407	Enzo Doria	06/2014
9818	6^113608-65	88405	Lelio R Paula	12/2015
9819	2^293624+82875	88390	Lelio R Paula	10/2013
9820	(2^293618+918)/2	88388	Stefano Morozzi	01/2020
9821	2^293612-112337	88387	Enzo Doria	06/2014
9822	758^30693+30693^758	88386	Norbert Schneider	05/2017
9823	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
9824	5*10^88377+77	88378	Robert Price	06/2016
9825	(2^293584+1558)/2	88378	Stefano Morozzi	01/2020
9826	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
9827	20918^16743+16743^20918	88355	Hans Havermann	08/2020
9828	(2^293499+2390)/2	88352	Stefano Morozzi	01/2020
9829	20727^18292+18292^20727	88344	Hans Havermann	08/2020
9831	2^293461-2785843	88341	Enzo Doria	03/2016
9830	(31*10^88340+257)/9	88341	Robert Price	12/2021
9833	2^293416-1037	88328	Yves Minet	11/2012
9832	6*10^88327+43	88328	Robert Price	07/2020
9834	(58*10^88321-49)/9	88322	Robert Price	05/2022
9835	25109^3292+3292^25109	88320	Hans Havermann	08/2020
9836	(2^293384-7)/3	88317	Lelio R Paula	01/2013
9837	(3^185092-5)/4	88311	Lelio R Paula	01/2013
9838	(5*10^88303-173)/3	88304	Robert Price	11/2017
9839	14^77039-57	88297	Lelio R Paula	11/2015
9840	3*10^88293-59	88294	Robert Price	10/2017
9841	5^126303+42	88283	Lelio R Paula	10/2015
9842	(88*10^88269+83)/9	88270	Robert Price	03/2022
9844	19^69025-18	88266	Theodore Burton	01/2006
9843	140^41128+139	88266	Norbert Schneider	04/2019
9845	5*10^88261-3	88262	Dmitry Domanov	11/2010
9846	(2^293195+2238)/2	88261	Stefano Morozzi	01/2020
9847	8^97731-7^(97731-1)	88260	Robert Price	04/2016
9848	5*10^88254+59	88255	Robert Price	09/2016
9849	4*3^184968-7	88253	Lelio R Paula	08/2014
9850	34*10^88251-9	88253	Robert Price	06/2020
9851	7^104426+88	88251	Lelio R Paula	10/2015
9852	2^293142+99	88245	Lelio R Paula	10/2012
9853	11^84736-2130	88244	Enzo Doria	12/2012
9854	23884^4945+4945^23884	88232	Hans Havermann	08/2020
9855	22080^9907+9907^22080	88231	Hans Havermann	08/2020
9856	(10^110315+1)/(10^22063+1)/5824812682167648578460281641	88225	Makoto Kamada	04/2019
9857	2^293068-89	88223	Lelio R Paula	10/2012
9858	2126^26511+26511^2126	88218	Norbert Schneider	02/2020
9859	2^293014-109655	88207	Enzo Doria	04/2014
9860	8*7^104371-3	88205	Lelio R Paula	10/2014
9861	2^292995-2145	88201	Lelio R Paula	10/2013
9862	28534^1233+1233^28534	88198	Hans Havermann	08/2020
9863	5*10^88182+77	88183	Robert Price	06/2016
9865	2^292929+43877	88181	Donovan Johnson	04/2005
9864	6^113321+131	88181	Lelio R Paula	12/2015
9866	(2^292919+3366)/2	88178	Stefano Morozzi	01/2020
9867	2^292904-583949	88173	Paul Bourdelais	04/2013
9868	2^292894-111851	88170	Enzo Doria	05/2014
9869	2^292872-2797349	88164	Enzo Doria	03/2016
9870	(2^292864+1042)/2	88161	Stefano Morozzi	01/2020
9871	2^292860-109685	88160	Enzo Doria	04/2014
9872	9*6^113288-5	88157	Lelio R Paula	10/2014
9873	(2^292735+2166)/2	88122	Stefano Morozzi	01/2020
9874	(2^292735+2346)/2	88122	Stefano Morozzi	01/2020
9875	(2^292705+1934)/2	88113	Stefano Morozzi	01/2020
9876	(2*10^88112-23)/3	88112	Robert Price	09/2017
9877	29622^943+943^29622	88111	Hans Havermann	08/2020
9878	(73*10^88105+17)/9	88106	Robert Price	10/2015
9879	(2^292673+3026)/2	88104	Stefano Morozzi	01/2020
9880	11^84588+78	88090	Lelio R Paula	11/2015
9881	(265*10^88077+11)/3	88079	Robert Price	03/2017
9882	91^44959-90^44959	88077	Robert Price	07/2015
9883	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
9884	1316^28233+28233^1316	88066	Norbert Schneider	07/2020
9885	(2^292543+2234)/2	88064	Stefano Morozzi	01/2020
9886	(10^88020+101)/3	88020	Robert Price	04/2016
9887	52^51285-51	88006	Norbert Schneider	09/2018
9888	21002^15501+15501^21002	88006	Hans Havermann	08/2020
9889	20466^19951+19951^20466	88004	Hans Havermann	08/2020
9890	(2^292324+2346)/2	87998	Stefano Morozzi	01/2020
9891	21634^11683+11683^21634	87998	Hans Havermann	08/2020
9892	(6340^23143-1)/6339	87988	Serge Batalov	08/2020
9893	20674^18013+18013^20674	87980	Hans Havermann	08/2020
9894	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
9895	(11*10^87960-41)/3	87961	Robert Price	12/2021
9896	(424*10^87930-1)/9	87932	Robert Price	11/2017
9897	(2^292100+3070)/2	87931	Stefano Morozzi	01/2020
9898	p(18225)#/2+128	87929	Robert Price	04/2017
9899	(10607^21841-1)/10606	87919	Serge Batalov	08/2020
9900	(2^292047+1550)/2	87915	Stefano Morozzi	01/2020
9901	4*6^112977+7	87914	Lelio R Paula	10/2014
9902	(2^292016+1062)/2	87906	Stefano Morozzi	01/2020
9903	(11359^21673-1)/11358	87888	Serge Batalov	08/2020
9904	14^76677+69	87882	Lelio R Paula	11/2015
9905	(22*10^87863-1)/3	87864	Robert Price	12/2014
9906	2^291822-2797811	87848	Enzo Doria	04/2016
9907	(22*10^87821-43)/3	87822	Robert Price	10/2021
9908	(2^291730+1614)/2	87820	Stefano Morozzi	01/2020
9909	(277*10^87817-7)/9	87819	Robert Price	02/2022
9910	2^291716-111389	87816	Enzo Doria	05/2014
9911	(782*10^87809-71)/9	87811	Robert Price	06/2017
9912	3^184039+1820	87809	Lelio R Paula	12/2015
9913	12^81356+41	87798	Lelio R Paula	11/2015
9914	21307^13188+13188^21307	87789	Hans Havermann	08/2020
9915	(2527^25801-1)/2526	87788	Serge Batalov	08/2020
9916	(2^291596+1986)/2	87779	Stefano Morozzi	01/2020
9918	6^112792-18983	87770	Enzo Doria	03/2013
9917	(3123^25117-1)/3122	87770	Serge Batalov	08/2020
9919	3*6^112787-5	87766	Lelio R Paula	10/2014
9920	7^103848+82	87762	Lelio R Paula	10/2015
9921	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
9922	(2^291506+918)/2	87752	Stefano Morozzi	01/2020
9923	24411^3932+3932^24411	87749	Hans Havermann	08/2020
9924	(3^183915+5)/128	87748	Lelio R Paula	01/2013
9925	19^68619+24	87747	Lelio R Paula	12/2015
9927	2^291480+1185	87745	Lelio R Paula	10/2013
9926	2^291482+1867369	87745	Enzo Doria	03/2016
9928	2^291467-937	87741	Yves Minet	05/2013
9929	(25*10^87726+161)/3	87727	Robert Price	01/2017
9930	11^84239-2850	87726	Enzo Doria	12/2012
9931	10^87720+215541	87721	Patrick De Geest	01/2011
9932	10^87720-3	87720	Markus Tervooren	07/2010
9933	(2^291383+3078)/2	87715	Stefano Morozzi	01/2020
9935	(5*10^87712-473)/9	87712	Robert Price	12/2017
9934	(2^291373+2946)/2	87712	Stefano Morozzi	01/2020
9936	22591^7630+7630^22591	87711	Hans Havermann	08/2020
9937	22081^9378+9378^22081	87709	Hans Havermann	08/2020
9938	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
9939	(2^291280+462)/2	87684	Stefano Morozzi	01/2020
9940	20749^16816+16816^20749	87680	Hans Havermann	08/2020
9941	93^44541-2	87679	Lelio R Paula	09/2013
9942	2^291261-109561	87679	Enzo Doria	04/2014
9943	(4*10^87669+149)/9	87669	Robert Price	03/2017
9944	2^291217+4257	87666	Lelio R Paula	10/2013
9945	22748^7137+7137^22748	87660	Hans Havermann	08/2020
9946	2*12^81214-5^81214	87645	Mike Oakes	12/2010
9947	(2^291150+2291)/15	87644	Eric Chen	08/2022
9948	(85*10^87637-139)/9	87638	Robert Price	08/2021
9949	(5005^23689-1)/5004	87632	Serge Batalov	08/2020
9950	(5*10^87622-473)/9	87622	Robert Price	12/2017
9951	12^81188+85	87617	Lelio R Paula	11/2015
9952	(2^291030+3462)/2	87609	Stefano Morozzi	01/2020
9953	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
9954	(2^290980+1150)/2	87594	Stefano Morozzi	01/2020
9955	2^290958+127	87588	Lelio R Paula	09/2012
9956	78531!4-8	87580	Robert Price	11/2019
9957	2^290923-67	87577	Lelio R Paula	09/2012
9958	3*10^87573-97	87574	Robert Price	08/2017
9959	(13*10^87565+11)/3	87566	Robert Price	05/2015
9960	(2^290881+1022)/2	87564	Stefano Morozzi	01/2020
9961	(2^290857-7)/55	87555	Lelio R Paula	01/2013
9962	(2^290808+1498)/2	87542	Stefano Morozzi	01/2020
9963	2^290802+82875	87541	Lelio R Paula	10/2013
9964	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
9965	3^183441+236	87524	Lelio R Paula	12/2015
9966	4*10^87513-69	87514	Robert Price	01/2022
9967	2^290618-33	87485	Lelio R Paula	09/2012
9968	(184*10^87473-1)/3	87475	Robert Price	02/2017
9969	2^290534-115151	87460	Enzo Doria	06/2015
9970	2^290512-109757	87453	Enzo Doria	04/2014
9971	(32*10^87448-41)/9	87449	Robert Price	05/2015
9972	(2^290493+3074)/2	87447	Stefano Morozzi	01/2020
9973	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
9974	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
9975	2^290426+82875	87427	Lelio R Paula	11/2013
9976	3*2^290415-7	87425	Lelio R Paula	08/2014
9978	10^87408+57	87409	Robert Price	03/2011
9977	2^290366+74779	87409	Enzo Doria	04/2016
9979	22284^8365+8365^22284	87409	Hans Havermann	08/2020
9980	10^87408-123569	87408	Patrick De Geest	07/2013
9981	21517^11536+11536^21517	87404	Hans Havermann	08/2020
9982	6*10^87396+77	87397	Robert Price	06/2020
9983	(2^290268+3882)/2	87380	Stefano Morozzi	01/2020
9984	2^290265+58905	87379	Lelio R Paula	10/2013
9985	7^103391+16	87376	Lelio R Paula	10/2015
9986	(115*10^87368-7)/9	87370	Robert Price	11/2017
9987	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
9988	8*7^103379+3	87367	Lelio R Paula	10/2014
9989	(2^290226+7)/71	87365	Lelio R Paula	01/2013
9990	(29*10^87355-89)/3	87356	Robert Price	01/2022
9991	(3216^24907-1)/3215	87354	Serge Batalov	08/2020
9992	(2^290160+2686)/2	87347	Stefano Morozzi	01/2020
9993	13^78407-30	87341	Lelio R Paula	11/2015
9994	4*10^87337-99	87338	Robert Price	12/2016
9995	7*10^87319+39	87320	Robert Price	07/2016
9996	3*5^124921+2	87317	Lelio R Paula	10/2014
9997	78315!4-16	87316	Robert Price	11/2019
9998	3^182984+88	87306	Lelio R Paula	12/2015
9999	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
10000	(10^87323-1)/305183363375761435053	87303	Anonymous	10/2020

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